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Characteristic_function_(probability_theory) abstract "In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the inverse Fourier transform of the probability density function. Thus it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the characteristic functions of distributions defined by the weighted sums of random variables.In addition to univariate distributions, characteristic functions can be defined for vector or matrix-valued random variables, and can also be extended to more generic cases.The characteristic function always exists when treated as a function of a real-valued argument, unlike the moment-generating function. There are relations between the behavior of the characteristic function of a distribution and properties of the distribution, such as the existence of moments and the existence of a density function.".
Characteristic_function_(probability_theory) thumbnail Sinc_simple.svg?width=300.
Characteristic_function_(probability_theory) wikiPageID "3229401".
Characteristic_function_(probability_theory) wikiPageLength "32583".
Characteristic_function_(probability_theory) wikiPageOutDegree "120".
Characteristic_function_(probability_theory) wikiPageRevisionID "680629006".
Characteristic_function_(probability_theory) wikiPageWikiLink Analytic_continuation.
Characteristic_function_(probability_theory) wikiPageWikiLink Bernoulli_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Bijection.
Characteristic_function_(probability_theory) wikiPageWikiLink Binomial_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Biometrika.
Characteristic_function_(probability_theory) wikiPageWikiLink Bochners_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Category:Probability_theory.
Characteristic_function_(probability_theory) wikiPageWikiLink Category:Theory_of_probability_distributions.
Characteristic_function_(probability_theory) wikiPageWikiLink Cauchy_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Central_Limit_Theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Central_limit_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Chi-squared_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Complex_conjugate.
Characteristic_function_(probability_theory) wikiPageWikiLink Complex_number.
Characteristic_function_(probability_theory) wikiPageWikiLink Conjugate_transpose.
Characteristic_function_(probability_theory) wikiPageWikiLink Continuity_set.
Characteristic_function_(probability_theory) wikiPageWikiLink Continuous_Fourier_transform.
Characteristic_function_(probability_theory) wikiPageWikiLink Continuous_dual.
Characteristic_function_(probability_theory) wikiPageWikiLink Convergence_in_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Convergence_of_random_variables.
Characteristic_function_(probability_theory) wikiPageWikiLink Convex_combination.
Characteristic_function_(probability_theory) wikiPageWikiLink Convex_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Cumulant.
Characteristic_function_(probability_theory) wikiPageWikiLink Cumulant_generating_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Cumulative_distribution_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Càdlàg.
Characteristic_function_(probability_theory) wikiPageWikiLink Degenerate_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Differentiable.
Characteristic_function_(probability_theory) wikiPageWikiLink Differentiable_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Dirichlet_integral.
Characteristic_function_(probability_theory) wikiPageWikiLink Discrete_random_variable.
Characteristic_function_(probability_theory) wikiPageWikiLink Dual_space.
Characteristic_function_(probability_theory) wikiPageWikiLink Duality_(mathematics).
Characteristic_function_(probability_theory) wikiPageWikiLink Expected_value.
Characteristic_function_(probability_theory) wikiPageWikiLink Exponential_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Fourier_inversion_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Fourier_transform.
Characteristic_function_(probability_theory) wikiPageWikiLink Gamma_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Hermite_polynomials.
Characteristic_function_(probability_theory) wikiPageWikiLink Hermitian_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Imaginary_unit.
Characteristic_function_(probability_theory) wikiPageWikiLink Indecomposable_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Independence_(probability_theory).
Characteristic_function_(probability_theory) wikiPageWikiLink Indicator_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Integrable_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Integral.
Characteristic_function_(probability_theory) wikiPageWikiLink Inverse_Fourier_transform.
Characteristic_function_(probability_theory) wikiPageWikiLink Kernel_embedding_of_distributions.
Characteristic_function_(probability_theory) wikiPageWikiLink Kernel_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Kluwer_Academic_Publishers.
Characteristic_function_(probability_theory) wikiPageWikiLink Laplace_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Law_of_large_numbers.
Characteristic_function_(probability_theory) wikiPageWikiLink Lebesgue-integrable.
Characteristic_function_(probability_theory) wikiPageWikiLink Lebesgue_integration.
Characteristic_function_(probability_theory) wikiPageWikiLink Lebesgue_measure.
Characteristic_function_(probability_theory) wikiPageWikiLink Lxc3xa9vys_continuity_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Lévy_continuity_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Lévy’s_continuity_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Maximum_likelihood.
Characteristic_function_(probability_theory) wikiPageWikiLink Measure_(mathematics).
Characteristic_function_(probability_theory) wikiPageWikiLink Moment-generating_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Moment_(mathematics).
Characteristic_function_(probability_theory) wikiPageWikiLink Multivariate_Cauchy_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Multivariate_normal_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Multivariate_random_variable.
Characteristic_function_(probability_theory) wikiPageWikiLink Negative_binomial_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Normal_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Poisson_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Positive-definite_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Positive-definite_kernel.
Characteristic_function_(probability_theory) wikiPageWikiLink Positive_definite_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Probability-generating_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Probability_density_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Probability_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Probability_theory.
Characteristic_function_(probability_theory) wikiPageWikiLink Quantile_function.
Characteristic_function_(probability_theory) wikiPageWikiLink Radon–Nikodym_derivative.
Characteristic_function_(probability_theory) wikiPageWikiLink Radon–Nikodym_theorem.
Characteristic_function_(probability_theory) wikiPageWikiLink Random_element.
Characteristic_function_(probability_theory) wikiPageWikiLink Random_matrix.
Characteristic_function_(probability_theory) wikiPageWikiLink Random_variable.
Characteristic_function_(probability_theory) wikiPageWikiLink Random_vector.
Characteristic_function_(probability_theory) wikiPageWikiLink Real-valued.
Characteristic_function_(probability_theory) wikiPageWikiLink Real_part.
Characteristic_function_(probability_theory) wikiPageWikiLink Reproducing_kernel_Hilbert_space.
Characteristic_function_(probability_theory) wikiPageWikiLink Riemann–Stieltjes_integral.
Characteristic_function_(probability_theory) wikiPageWikiLink Smoothness_(probability_theory).
Characteristic_function_(probability_theory) wikiPageWikiLink Springer_Science+Business_Media.
Characteristic_function_(probability_theory) wikiPageWikiLink Stable_distribution.
Characteristic_function_(probability_theory) wikiPageWikiLink Statistical_independence.
Characteristic_function_(probability_theory) wikiPageWikiLink Statistics.
Characteristic_function_(probability_theory) wikiPageWikiLink Stochastic_process.
Characteristic_function_(probability_theory) wikiPageWikiLink Subindependence.
Characteristic_function_(probability_theory) wikiPageWikiLink Time_series.